probability maths

Question

There are 150 words on a page, 30 are nouns, 10 of which start with a vowel. Of the words that are not nouns, 85 of them do not start with vowels.

If a word on the page starts with a vowel, what is the probability that it is a noun?

Answer 1

P(V/N) =10/30= 1/3

P(N) = 30/150= 1/5

P(V) = 30+85/150 = 115/150 = 23/30

P(V/~N) =85/(150-50)= .85 = 17/20

P(~N) =120/150= 4/5

P(N/V)=2/23= about 8.7%

use Bayes Theorem. General formula is P(x/y)P(y) = P(y/x)P(x) let x=N, y=V

P(N/V)P(V) = P(V/N)P(N)

P(N/V) = P(V/N)P(N)/P(V) = (1/3)(1/5)/(23/30)

= (1/15)/(23/30) = (1/15)(30/23 = 2/23

this is deductive logic. avoiding the inductive problem of conventional statistics

thank a monk Rev. Bayes, for coming up with this formula.

if you got stuck with child support based on a blood test they use Bayes Theorem to prove you're the dad. If you think it's another father, go for the DNA test, it's far more reliable. Reverend Thomas Bayes was an Evil monk. maybe.